If rocket damage is a concern, why don’t such rockets destroy themselves right after leaving the launchpad? At that point the water suppression is no longer relevant but the sound waves are just as powerful. It can’t just be that the ground reflects sound waves, since that would only be a ≈3dB (2x) increase in sound energy. Rockets with >2x more thrust seem to use the same sound suppression, so rocket damage can’t be the main reason for installing such systems.

My guess is that water systems are needed to reduce damage to the launch pad.